Structural Realism

Structural realism is considered by many realists and antirealists
alike as the most defensible form of scientific realism. There are now
many forms of structural realism and an extensive literature about
them. There are interesting connections with debates in metaphysics,
philosophy of physics and philosophy of mathematics. This entry is
intended to be a comprehensive survey of the field.

Scientific realism is the view that we ought to believe in the
unobservable entities posited by our most successful scientific
theories. It is widely held that the most powerful argument in favour
of scientific realism is the no-miracles argument, according to which
the success of science would be miraculous if scientific theories were
not at least approximately true descriptions of the world. While the
underdetermination argument is often cited as giving grounds for
scepticism about theories of unobservable entities, arguably the most
powerful arguments against scientific realism are based on the history
of radical theory change in science. The best-known of these arguments,
although not necessarily the most compelling of them, is the notorious
pessimistic meta-induction, according to which reflection on the
abandonment of theories in the history of science motivates the
expectation that our best current scientific theories will themselves
be abandoned, and hence that we ought not to assent to them.

Structural realism was introduced into contemporary philosophy of
science by John Worrall in 1989 as a way to break the impasse that
results from taking both arguments seriously, and have “the best
of both worlds” in the debate about scientific realism. With
respect to the case of the transition in nineteenth-century optics
from Fresnel's elastic solid ether theory to Maxwell's theory of the
electromagnetic field, Worrall argues that:

There was an important element of continuity in the shift from
Fresnel to Maxwell—and this was much more than a simple
question of carrying over the successful empirical content into the new
theory. At the same time it was rather less than a carrying over of the
full theoretical content or full theoretical mechanisms (even in
“approximate” form) … There was continuity or
accumulation in the shift, but the continuity is one of form or
structure, not of content. (1989, 117)

According to Worrall, we should not accept standard scientific
realism, which asserts that the nature of the unobservable objects that
cause the phenomena we observe is correctly described by our best
theories. However, neither should we be antirealists about science.
Rather, we should adopt structural realism and epistemically commit
ourselves only to the mathematical or structural content of our
theories. Since there is (says Worrall) retention of structure across
theory change, structural realism both (a) avoids the force of the
pessimistic meta-induction (by not committing us to belief in the
theory's description of the furniture of the world) and (b) does
not make the success of science (especially the novel predictions of
mature physical theories) seem miraculous (by committing us to the
claim that the theory's structure, over and above its empirical
content, describes the world).

Worrall's paper has been widely cited and has spawned an
extensive literature in which various varieties of structural realism
are advocated. These contemporary debates recapitulate the work of some
of the greatest philosophers of science. Worrall says he found his
structural realism in Henri Poincaré (1905, 1906) whose
structuralism was combined with neo-Kantian views about the nature of
arithmetic and group theory, and with conventionalism about the
geometry of space and time. (The prevalence of Kantian themes in the
literature on structural realism is discussed further below; for more
on Poincaré see Giedymin 1982, Gower 2000 and Zahar 1994, 2001.)
Ernan McMullin (1990) argues that Pierre Duhem was a realist about the
relations found in laws but not about explanations in terms of an
ontology. According to Worrall (1989), Barry Gower (2000) and Elie
Zahar (2001), Duhem too was a kind of structural realist, though there
are passages in Duhem that more readily lend themselves to an
instrumentalist interpretation. Gower's (2000) historical survey
of structural realism also discusses how structuralism figures in the
thought of Ernst Cassirer, Moritz Schlick, Rudolf Carnap and Bertrand
Russell. Stathis Psillos (1999) has explored the connections between
structuralism and the Ramsey-sentence approach to scientific theory as
it figured in the development of Carnap's philosophy from logical
positivism to ontologically relativist empiricism. Other important
pioneers of structuralism about science include Arthur Eddington (see
French 2003), Grover Maxwell (see Ladyman 1998 and 3.1 below) and
Hermann Weyl (see Ryckman 2005).

Ladyman (1998) distinguished epistemic and ontic forms of structural
realism, and many of those who have taken up structural realism have
been philosophers of physics who have developed the latter. Others have
made it clear that their structural realism is a purely epistemological
refinement of scientific realism. On the other hand, Bas van Fraassen
(1997, 2006, 2008) defends an empiricist and non-realist form of
structuralism about science, motivated by an illuminating
reconstruction of the origins of structuralism in the debate about the
epistemology of physical geometry in the nineteenth century, and more
generally in the progressive mathematisation of science. Yet more kinds
of structuralism now abound in contemporary analytic philosophy. These
include causal structuralism concerning the individuation of
properties, mathematical structuralism concerning the nature of
mathematical objects, and structuralism about laws and dispositions.
The relationship between structural realism and these views is a matter
for further work. While many realists and antirealists alike are agreed
that the most viable form of scientific realism is structural realism,
many others continue to defend other forms of scientific realism. This
article reviews the issues and provides a guide for further
reading.

Scientific realism became dominant in philosophy of science after
the demise of the forms of antirealism about science associated with
the logical positivists, namely semantic instrumentalism, according to
which theoretical terms are not to be interpreted as referring to
anything, and theoretical reductionism, according to which theoretical
terms are disguised ways of referring to observable phenomena. These
forms of antirealism rely upon discredited doctrines about scientific
language, such as that it can be divided into theoretical and
observational parts, and that much of it should not be taken literally.
Bas van Fraassen (1980) revitalised the debate about scientific realism
by proposing his constructive empiricism as an alternative. His
antirealism is sceptical rather than dogmatic, and does not depend on
the distinction between theoretical and observational terms. He allows
that terms such as ‘sub-atomic particle’ and
‘particle too small to see’ are perfectly meaningful and
should be taken literally (note that the former term is theoretical and
the latter term is not but both purportedly refer to unobservable
entities). On the other hand, he holds that it is perfectly rational to
remain agnostic about whether there are any such particles because he
argues that to accept the best scientific theories we have only
requires believing that they are empirically adequate, in the sense of
correctly describing the observable world, rather than believing that
they are true simpliciter. (For more on constructive empiricism see
Monton 2007.)

How then are we to decide whether to believe in the full theoretical
truth of scientific theories, including what they say about
unobservable entities such as electrons and black holes, or whether to
believe instead merely that our best scientific theories are
empirically adequate? Van Fraassen argues that since the latter belief
is logically weaker and yet as empirically contentful as the former belief
it is natural for an empiricist to go only as far as belief in
empirical adequacy. On the other hand, many philosophers are moved by
the fact that belief in only the empirical adequacy of our best
scientific theories leaves us unable to explain the phenomena that they
describe. Inference to the best explanation is widely believed to be an
important form of reasoning in science, and the production of
explanations of the world is often supposed to be one of the main
successes of science. When the target of explanation becomes science
itself and its history of empirical success as a whole, we arrive at
the no-miracles argument famously presented by Hilary Putnam as
follows: “The positive argument for realism is that it is the
only philosophy that doesn't make the success of science a
miracle” (1975, 73).

The no-miracles argument is elaborated in terms of specific features
of scientific methodology and practice. Richard Boyd (1985, for
example) argues that in explaining the success of science, we need to
explain the overall instrumental success of scientific methods across
the history of science. Alan Musgrave (1988) says that the only version
of the no-miracles argument that might work is one appealing to the
novel predictive success of theories. Some realists, such as Psillos
(1999), have gone so far as to argue that only theories which have
enjoyed novel predictive success ought to be considered as falling
within the scope of arguments for scientific realism.

Colin Howson (2000), P.D. Magnus and Craig Callender (2004), and
Peter Lipton (2004) have recently argued that the no-miracles argument
is flawed because in order to evaluate the claim that it is probable
that theories enjoying empirical success are approximately true we have
to know what the relevant base rate is, and there is no way we can know
this. Magnus and Callender argue that “wholesale” arguments
that are intended to support realism (or antirealism) about science as
a whole (rather than “retail” arguments that are applied to
a specific theory) are only taken seriously because of our propensity
to engage in the ‘base rate fallacy’ of evaluating
probabilities without knowing all the relevant information. They think
we ought to abandon the attempt to defend scientific realism in general
rather than on a case-by-case basis.

When it comes to wholesale arguments against scientific
realism, perhaps the most influential until recently was the
underdetermination argument, according to which the existence of
empirical equivalents to our best scientific theories implies that we
should withhold epistemic commitment to them. This is often dismissed
by realists as generating doubt about unobservables that is no more
worrying than doubting other minds or the external world. They argue
that since scientists find ways of choosing between empirically
equivalent rivals, philosophers ought not to make too much of merely
in-principle possibilities that are irrelevant to scientific practice
(see Laudan and Leplin 1991, 1993, and Kukla 1998). (Kyle Stanford
(2006) defends an underdetermination argument called ‘the
problem of unconceived alternatives’ with reference to the
history of science, so perhaps not all underdetermination arguments
are a priori and theoretical.)

The power of the arguments against scientific realism from theory
change is that, rather than being a priori and theoretical, they are
empirically based and their premises are based on data obtained by
examining the practice and history of science. Ontological
discontinuity in theory change seems to give us grounds not for mere
agnosticism but for the positive belief that many central theoretical
terms of our best contemporary science will be regarded as
non-referring by future science. So-called ‘pessimistic
meta-inductions’ about theoretical knowledge take many forms and
are probably almost as ancient as scepticism itself. They have the basic
form:

Proposition p is widely believed by most contemporary
experts, but p is like many other hypotheses that were widely
believed by experts in the past and are disbelieved by most
contemporary experts. We have as much reason to expect p to
befall their fate as not, therefore we should at least suspend
judgement about p if not actively disbelieve it.

More precisely, Larry Laudan (1981) gave a very influential argument
with the following structure:

There have been many empirically successful theories in the history of
science which have subsequently been rejected and whose theoretical
terms do not refer according to our best current theories.

Our best
current theories are no different in kind from those discarded theories
and so we have no reason to think they will not ultimately be replaced
as well.

So, by induction we have positive reason to expect that our best
current theories will be replaced by new theories according to which
some of the central theoretical terms of our best current theories do
not refer, and hence we should not believe in the approximate truth or
the successful reference of the theoretical terms of our best current
theories.

The most common realist response to this argument is to restrict
realism to theories with some further properties (usually, maturity,
and novel predictive success) so as to cut down the inductive base
employed in (i) (see Psillos 1996). Moreover Peter Lewis (2001), Marc
Lange (2002) and Magnus and Callender (2004) regard the pessimistic
meta-induction as a fallacy of probabilistic reasoning. However, there
are arguments from theory change that are not probabilistic. Note first
that there are several cases of mature theories which enjoyed novel
predictive success, notably the ether theory of light and the caloric
theory of heat. If their central theoretical terms do not refer, the
realist's claim that approximate truth explains empirical success
will no longer be enough to establish realism, because we will need
some other explanation for the success of the caloric and ether theories.
If this will do for these theories then it ought to do for others where
we happened to have retained the central theoretical terms, and then we
do not need the realist's preferred explanation that such
theories are true and successfully refer to unobservable entities.

Laudan's paper was also intended to show that the successful
reference of its theoretical terms is not a necessary condition for the
novel predictive success of a theory (1981, 45), and there are
counter-examples to the no-miracles argument.

Successful reference of its central
theoretical terms is a necessary condition for the approximate truth of
a theory.

There are examples of theories that were
mature and had novel predictive success but whose central theoretical
terms do not refer.

So there are examples of theories that
were mature and had novel predictive success but which are not
approximately true.

Approximate truth and successful reference of
central theoretical terms is not a necessary condition for the
novel-predictive success of scientific theories

So, the no-miracles argument is undermined since, if approximate
truth and successful reference are not available to be part of the
explanation of some theories' novel predictive success, there is
no reason to think that the novel predictive success of other theories
has to be explained by realism.

There are two common (not necessarily exclusive) responses to
this:

(I) Develop an account of reference according to which the
abandoned theoretical terms are regarded as successfully referring
after all.

Realists developed causal theories of reference to account for
continuity of reference for terms like ‘atom’ or
‘electron’, even though the theories about atoms and
electrons have undergone significant changes. The difference with the terms
‘ether’ and ‘caloric’ is that they are no
longer used in modern science. However, as C.L. Hardin and Alexander
Rosenberg (1982) argue, the causal theory of reference may be used to
defend the claim that terms like ‘ether’ referred to whatever
causes the phenomena responsible for the terms' introduction.
This is criticized by Laudan (1984) as making the reference of
theoretical terms a trivial matter, since as long as some phenomena
prompt the introduction of a term it will automatically successfully
refer to whatever is the relevant cause (or causes). Furthermore, this
theory radically disconnects what a theorist is talking about from what
she thinks she is talking about. For example, Aristotle or Newton could
be said to be referring to geodesic motion in a curved spacetime when,
respectively, they talked about the natural motion of material objects,
and the fall of a body under the effect of the gravitational force.

(II) Restrict realism to those parts of theories that play an
essential role in the derivation of subsequently observed (novel)
predictions, and then argue that the terms of past theories which are
now regarded as non-referring were non-essential and hence that there
is no reason to deny that the essential terms in current theories will
be retained. Philip Kitcher says that: “[n]o sensible realist
should ever want to assert that the idle parts of an individual
practice, past or present, are justified by the success of the
whole” (1993, 142).

The most detailed and influential response to the argument from
theory change is due to Psillos (1999), who combines strategies (I) and
(II). Hasok Chang (2002), Kyle Stanford (2002 and 2003), Mohammed
Elsamahi (2005) and Timothy Lyons (2006) criticize Psillos's
account. Other responses include Kitcher's (1993) model of
reference according to which some tokens of theoretical terms refer and
others do not. Christina McLeish (2005) criticizes Kitcher's
theory by arguing that there are no satisfactory grounds for making the
distinction between referring and non-referring tokens. McLeish (2006)
argues that abandoned theoretical terms like ‘ether’
partially refer and partially fail to refer. Juha Saatsi (2005) denies
premise (a) and claims that there can be approximate truth of the
causal roles postulated by a scientific theory without its central
terms necessarily successfully referring (see also Chakravartty, 1998).

There is no consensus among those defending standard realism in the
face of theory change. The argument from theory change threatens
scientific realism because if what science now says is correct, then
the ontologies of past scientific theories are far from accurate
accounts of the furniture of the world. If that is so even though they
were predictively successful, then the success of our best current
theories does not mean they have got the nature of the world right
either. The structuralist solution to this problem is to give up the
attempt to learn about the nature of unobservable entities from
science. The metaphysical import of successful scientific theories
consists in their giving correct descriptions of the structure of the
world. Theories can be very different and yet share all kinds of
structure. The task of providing an adequate theory of approximate
truth that fits the history of science and directly addresses the
problem of ontological continuity has hitherto defeated realists, but
a much more tractable problem is to display the structural
commonalities between different theories. Hence, a form of realism
that is committed only to the structure of theories might not be
undermined by theory change. Gerhard Schurz (2009) proves a structural
correspondence theorem showing that successive theories that share
empirical content also share theoretical content. (McArthur (2011)
argues that structural realism eliminates both theory change in
science and scientific discovery.)

There are numerous examples of continuity in the mathematical
structure of successive scientific theories. Indeed Niels Bohr and
others explicitly applied the methodological principle known as the
‘correspondence principle’, according to which
quantum-mechanical models ought to mathematically reduce to classical
models in the limit of large numbers of particles, or the limit of
Planck's constant becoming arbitrarily small. There are many cases in
quantum mechanics where the Hamiltonian functions that represent the
total energy of mechanical systems imitate those of classical
mechanics, but with variables like those that stand for position and
momentum replaced by Hermitian operators. Simon Saunders (1993a)
discusses the structural continuities between classical and quantum
mechanics and also shows how much structure Ptolemaic and Copernican
astronomy have in common. Harvey Brown (1993) explains the
correspondence between Special Relativity and classical
mechanics. Jonathan Bain and John Norton (2001) discuss the structural
continuity in descriptions of the electron, as does Angelo Cei
(2004). Votsis (2011) considers examples of continuity and
discontinuity in physics.
Robert Batterman (2002) discusses many examples of limiting
relationships between theories, notably the renormalization group
approach to critical phenomena, and the relationship between wave and
ray optics. Holger Lyre (2004) extends Worrall's original example of
the continuity between wave optics and electromagnetism by considering
the relationship between Maxwellian electrodynamics and Quantum
Electrodynamics. Saunders (2003c and d) also criticises Tian Cao
(1997) for underestimating the difficulties with a non-structuralist
form of realism in the light of the history of quantum field
theory.

The most minimal form of structuralism focuses on empirical
structure, and as such is best thought of as a defence of the
cumulative nature of science in the face of Kuhnian worries about
revolutions (following Post 1971). See Katherine Brading's and
Elaine Landry's (2006) ‘minimal structuralism’, and
Otavio Bueno's (1999, 2000) and van Fraassen's (2006, 2007,
2008) structural empiricism (Ryckman 2005 calls the latter
“instrumental structuralism”).

Structural realism is often characterised as the view that
scientific theories tell us only about the form or structure of the
unobservable world and not about its nature. This leaves open the
question as to whether the natures of things are posited to be
unknowable for some reason or eliminated altogether. Hence, Ladyman
(1998) raised the question as to whether Worrall's structural
realism is intended as a metaphysical or epistemological modification
of standard scientific realism. Worrall's paper is ambiguous in
this respect. That he has in mind only an epistemic constraint on
realism—commitment to the structure of our best scientific
theories but agnosticism about the rest of the content—is
suggested by his citation of Poincaré who talks of the redundant
theories of the past capturing the “true relations” between
the “real objects which Nature will hide forever from our
eyes” (1905, 161). So one way of thinking about structural
realism is as an epistemological modification of scientific realism to
the effect that we only believe what scientific theories tell us about
the relations entered into by unobservable objects, and suspend
judgement as to the nature of the latter. (ESR is called
‘restrictive structural realism’ by Psillos 2001.) There
are various forms this might take. (See French and Ladyman 2011.)

We cannot know the individuals that
instantiate the structure of the world but we can know their properties
and relations.

We cannot know the individuals or their
intrinsic/non-relational properties but we can know their first-order
relational properties.

We cannot know the individuals, their
first-order properties or relations, but we can know the second-order
structure of their relational properties. Russell (1927) and Carnap
(1928) took this extreme view and argued that science only tells us
about purely logical features of the world.

Psillos (2001) refers to the “upward path” to structural
realism as beginning with empiricist epistemological principles and
arriving at structural knowledge of the external world. The
“downward” path is to arrive at structural realism by
weakening standard scientific realism as suggested by Worrall. Both
paths are criticized by Psillos. Russell (1927) was led along the
upward path by three epistemological principles: firstly, the claim
that we only have direct access to our percepts (Ayer's
‘egocentric predicament’); secondly, the principle that
different effects have different causes (which is called the
Helmholtz-Weyl Principle by Psillos); and thirdly, that the relations
between percepts have the same logico-mathematical structure as the
relations between their causes. This led him to the claim that science
can only describe the world up to isomorphism, and hence to (3) above
since according to him we know only the (second-order) isomorphism
class of the structure of the world and not the (first-order) structure
itself. Russell's upward path is defended by Votsis (2005).

Mauro Dorato argues for ESR on the grounds that structural realism
needs entity realism to be plausible (1999, 4). Most defenders of ESR
assume that there must be individual objects and properties that are
ontologically prior to relational structure. Matteo Morganti differs
from other epistemic structural realists by arguing for agnosticism
about whether there is a domain of individuals over and above
relational structure.

As mentioned above, Poincaré's structuralism had a Kantian
flavour. In particular, he thought that the unobservable entities
postulated by scientific theories were Kant's noumena or things in
themselves. He revised Kant's view by arguing that the latter can be
known indirectly rather than not at all because it is possible to know
the relations into which they enter. Poincaré followed the
upward path to structural realism, beginning with the neo-Kantian goal
of recovering the objective or intersubjective world from the world
from the subjective world of private sense impressions: “what we
call objective reality is… what is common to many thinking
beings and could be common to all; … the harmony of
mathematical laws” (1906, 14). However, he also followed the
downward path to structural realism arguing that the history of
science can be seen as cumulative at the level of relations rather
than objects. For example, between Carnot's and Clausius'
thermodynamics the ontology changes but the Second Law of
Thermodynamics is preserved. While Worrall never directly endorses the
Kantian aspect of Poincaré's thought, Zahar's structural
realism is explicitly a form of Kantian transcendental idealism
according to which science can never tell us more than the structure
of the noumenal world; the nature of the entities and properties of
which it consists are epistemically inaccessible to us (as in (2)
above). Michaela Massimi (2011) develops a neo-Kantian perspective on
structural realism.

Frank Jackson (1998), Rae Langton (1998) and David Lewis
(2009) also advocate views similar to ESR. Jackson refers to
‘Kantian physicalism’ (1998: 23–24), Langton to
‘Kantian Humility’, and Lewis to ‘Ramseyan
Humility’. Peter Unger (2001) also argues that our knowledge of
the world is purely structural and that qualia are the non-structural
components of reality. Jackson argues that science only reveals the
causal / relational properties of physical objects, and that “we
know next to nothing about the intrinsic nature of the world. We know
only its causal cum relational nature” (1998: 24). Langton argues
that science only reveals the extrinsic properties of physical objects,
and both then argue that their intrinsic natures, and hence the
intrinsic nature of the world, are epistemically inaccessible. Jackson
points out that this inference can be blocked if the natures of objects
and their intrinsic properties are identified with their relational or
extrinsic properties, but argues that this makes a mystery of what it
is that stands in the causal relations. Lewis' structuralism is
based on the centrality he gives to the Ramsey sentence reconstruction
of scientific theories that is the subject of the next section.

A position called structural realism, that amounts to an
epistemological gloss on traditional scientific realism, was advocated
by Grover Maxwell (1962, 1970a, 1970b, 1972). Maxwell wanted to make
scientific realism compatible with “concept empiricism”
about the meaning of theoretical terms, and he also wanted to explain
how we can have epistemic access to unobservable entities. The problem
as Maxwell saw it was that theories talk about all sorts of entities
and processes with which we are not ‘acquainted’. How, he
wondered, can we then know about and refer to them and their
properties? The answer that he gave, following Russell, was that we
can know about them by description, that is we can know them via their
structural properties. In fact, he argues, this is the limit of our
knowledge of them, and the meanings of theoretical terms are to be
understood purely structurally. The way that Maxwell explicates the
idea that the structure of the theory exhausts the cognitive content
of its theoretical terms, is to consider the Ramsey sentence of the
theory (Ramsey 1929). Ramsey's method allows the elimination of
theoretical terms from a theory by replacing them with existentially
quantified predicate variables (or names in the case of the
influential Lewis 1970). If one replaces the conjunction of assertions
of a first-order theory with its Ramsey sentence, the observational
consequences of the theory are carried over, but direct reference to
unobservables is eliminated.

If we formalise a theory in a first-order language:
∏(O1,…,On;T1,…,Tm),
where the Os are the observational terms and the Ts
are the theoretical terms, then the corresponding Ramsey sentence is
∃t1,…,tm∏(O1,…,On;t1,…,tm). Thus
the Ramsey sentence only asserts that there are some objects,
properties and relations that have certain logical features,
satisfying certain implicit definitions. It is a higher-order
description, but ultimately connects the theoretical content of the
theory with observable behaviour. However, it is a mistake to think
that the Ramsey sentence allows us to eliminate theoretical entities,
for it still states that these exist. It is just that they are
referred to not directly, by means of theoretical terms, but by
description, that is via variables, connectives, quantifiers and
predicate terms whose direct referents are (allegedly) known by
acquaintance. Thus Maxwell (and Russell) claimed that knowledge of the
unobservable realm is limited to knowledge of its structural rather
than intrinsic properties, or, as is sometimes said, limited to
knowledge of its higher-order properties. It is arguable that this is
the purest structuralism possible, for the notion of structure
employed refers to the higher-order properties of a theory, those that
are only expressible in purely formal terms.

This is an epistemological structural realism meant to vindicate and
not to revise the ontological commitments of scientific realism. On
this view the objective world is composed of unobservable objects
between which certain properties and relations obtain; but we can only
know the properties and relations of these properties and relations,
that is, the structure of the objective world. However, there are
serious difficulties with this view which were originally raised by
Newman in 1928 and which have been recently discussed by Demopoulos and
Friedman (1989). The basic problem is that structure is not sufficient
to uniquely pick out any relations in the world. Suppose that the world
consists of a set of objects whose structure is W with respect to some
relation R, about which nothing else is known. Any collection of things
can be regarded as having structure W provided there is the right
number of them. This is because according to the extensional
characterisation of relations defined on a domain of individuals, every
relation is identified with some set of subsets of the domain. The
power set axiom entails the existence of every such subset and hence
every such relation.

As Demopoulos and Friedman point out, if ∏ is consistent, and
if all its purely observational consequences are true, then the truth
of the corresponding Ramsey sentence follows as a theorem of
second-order logic or set theory (provided the initial domain has the
right cardinality—and if it does not then consistency implies
that there exists one that does). The formal structure of a relation
can easily be obtained with any collection of objects provided there
are enough of them, so having the formal structure cannot single out a
unique referent for this relation; in order to do so we must stipulate
that we are talking about the intended relation, which is to go beyond
the structural description. “Thus on this view, only cardinality
questions are open to discovery!” (1989, 188); everything else
will be known a priori.

This leads Demopoulos and Friedman to conclude that reducing a
theory to its Ramsey sentence is equivalent to reducing it to its
empirical consequences, and thus that: “Russell's realism
collapses into a version of phenomenalism or strict empiricism after
all: all theories with the same observational consequences will be
equally true” (1985, 635). Similarly, Jane English (1973) argued,
though on the basis of different considerations, that any two Ramsey
sentences that are incompatible with one another cannot have all their
observational consequences in common. Hence it seems that if we treat a
theory just as its Ramsey sentence then the notion of theoretical
equivalence collapses onto that of empirical equivalence. (Demopoulos
2003 argues that similar considerations show that structural empiricism
also collapses truth to empirical adequacy; he also discusses the
relationship between Newman's problem and Putnam's Paradox.
Votsis 2003 argues that the conclusion of the Newman argument
doesn't undermine ESR after all. Gordon Solomon 1989 defends
Richard Braithwaite's claim that Eddington's structuralism
(see 4.1 below) is vulnerable to Newman's argument.)

Jeffery Ketland (2004) argues in detail that the Newman objection
trivialises the Ramsey sentence formulation of ESR. Worrall and Zahar
(2001) argue that the cognitive content of a theory is exhausted by
its Ramsey sentences but that, while the Ramsey sentence only
expresses the empirical content of the theory, the notion of empirical
content in play here is sufficient for a form of realism. In his 2007
paper, Worrall sets out an account and defense of epistemic structural
realism and responds to objections that have been raised to it,
including the Newman problem. Cruse (2005) and Melia and Saatsi (2006)
defend the Ramsey sentence approach against model-theoretic arguments
by questioning the assumption that all predicates which apply to
unobservables must be eliminated in favour of bound variables. Mixed
predicates such as ‘extended’ are those that apply to both
observable and unobservable objects. The Newman objection does not go
through if mixed predicates are not Ramsified, because a model of the
Ramsey sentence will not necessarily be one in which what is claimed
regarding the mixed properties and relations holds. In response,
Demopoulos (2008) points out that the Ramsey sentence of a theory with
mixed predicates where the latter are not Ramsified will be true
provided the original theory is satisfied—hence the claim that
the content of the Ramsey sentence is merely the observational content
of the original theory plus a cardinality claim is still true when
mixed predicates are considered. Melia and Saatsi (2006) also argue
that intensional notions, such as naturalness and causal significance,
may be applied to properties to save the Ramsey sentence formulation
of ESR from triviality. (This recalls the defence of Russell's
structuralism against Newman discussed in Hochberg 1994.) Demopoulos
also raises two problems with this strategy: firstly, even non-natural
relations can have significant claims made about them in a theory, and
secondly, the cognitive significance of unramsified theories is
independent of a commitment to ‘real’ or
‘natural’ relations. Hence, Demopoulos insists that the
Ramsey sentence of a theory and the theory itself are importantly
different (see also Psillos 2006b). Peter Ainsworth (2009) gives a
clear and accessible account of the Newman problem and the responses
that have been given to it. In his (2011) Demopoulos argues that there
are three very different views in the work of Russell, Ramsey, and
Carnap respectively, which have in common versions of a core
structuralist thesis that he identifies. All the accounts he considers
make use of Ramsey sentences; Demopoulos investigates the logical
properties of the Ramsey sentence and arrives at an argument against
the structuralist thesis. Friedman (2011) argues that Carnap’s account
of theoretical terms involving the Ramsey sentence approach is not
vulnerable to the Newman problem. The relationship between Friedman's
views on the relativized a priori and structural realism is
interrogated in Ivanova (2011).

Versions of ESR that employ the Ramsey sentence of a theory and the
distinction between observational and theoretical terms are embedded
in the so-called syntactic view of theories that adopts first-order
quantificational logic as the appropriate form for the representation
of physical theories. According to Zahar (1994, 14) the continuity in
science is in the intension rather than the extension of its
concepts. He argues that if we believe that the mathematical structure
of theories is fundamentally important for ontology, then we need a
semantics for theories that addresses the representative role of
mathematics directly. Such an account of scientific representation is
allegedly found in the so-called ‘semantic’ or
‘model-theoretic’ approach associated primarily with
Patrick Suppes, Fred Suppe, Ron Giere and Bas van Fraassen (see da
Costa and French 2003). The relationship between structuralism and the
semantic view is discussed by van Fraassen (1997, 2008), and
Thomson-Jones (2011). Chris Pincock (2011) criticises structural
realism on the basis of an analysis of the role of mathematics in
scientific representation. Ladyman (1998), and Ladyman and Ross (2007)
argue that the Newman problem does not arise for ontic structural
realism since it eschews an extensional understanding of
relations.

Ladyman (1998) argues that in general epistemological forms of
structural realism do not significantly improve the prospects of
standard scientific realism and that hence structural realism should be
thought of as metaphysically rather than merely epistemically
revisionary. Structural realism is supposed to help with the problem of
theory change. As Maxwell himself pointed out, his structural realism
is a purely semantic and epistemological theory. The Ramsey sentence
picks out exactly the same entities as the original theory. It does not
dispense with reference, but it makes that reference a function of the
(place of the theoretical terms in the) overall structure of the
theory, as manifested in the Ramsey sentence. The problem of
ontological discontinuity is left untouched by simply adopting
Ramsification. In fact, it seems even worse if contextualism about the
meaning of theoretical terms is adopted. Cei and French (2006) and
Cruse (2005) also argue, on different grounds, that Ramsification is of
no help to the structural realist.

Worrall's position in his 1989 paper is not explicitly an
epistemic one, and other comments suggest a different view: “On
the structural realist view what Newton really discovered are the
relationships between phenomena expressed in the mathematical equations
of his theory” (1989, 122). If the continuity in scientific
change is of “form or structure”, then perhaps we should
abandon commitment to even the putative reference of theories to
objects and properties, and account for the success of science in other
terms. Others who have contributed to structural realism have more
explicitly signalled a significant departure from traditional realist
metaphysics. For example, Howard Stein:

[O]ur science comes closest to comprehending ‘the real’,
not in its account of ‘substances’ and their kinds, but in
its account of the ‘Forms’ which phenomena
‘imitate’ (for ‘Forms’ read ‘theoretical
structures’, for ‘imitate’, ‘are represented
by’). (1989, 57).

A crude statement of ESR is the claim that all we know is the
structure of the relations between things and not the things
themselves, and a corresponding crude statement of OSR is the claim
that there are no ‘things’ and that structure is all there
is (this is called ‘radical structuralism’ by van Fraassen
2006).

OSR has attracted most sympathy among some philosophers of physics
and physicists. This is natural since, while Worrall's motivation
for introducing structural realism was solely the need for a realist
response to the pessimistic meta-induction, French and Ladyman
introduced OSR to describe a form of structural realism motivated by
two further problems:

identity and individuality of quantum
particles and spacetime points, and entanglement;

scientific representation, in particular the
role of models and idealisations in physics.

Their concern with (a) followed that of many of the pioneers of
structuralism in twentieth-century philosophy of science including
Cassirer, Eddington and Weyl. (Russell's and Carnap's versions of
structuralism were more directly motivated by epistemological and
semantic problems than by ontological issues arising from physics.)
French did seminal work on the identity and individuality of quantum
particles with Michael Redhead (who also wrote a classic paper on
theories and models (1980) and later endorsed structural realism as a
way of interpreting quantum field theory (1999)). More recently it has
become more widespread to advocate OSR as a response to contemporary
physics as a whole (for example, see Tegmark 2007). Among others who
have defended versions of OSR are Jonathan Bain (2003 and 2004),
Michael Esfeld (2004) and Esfeld and Lam (2008), Aharon Kantorovich
(2003), Holgar Lyre (2004), Gordon McCabe (2007) and John Stachel
(2002 and 2006). Saunders and David Wallace have deployed
structuralism to solve the problem of how macroscopic objects with
more or less determinate properties can be recovered from the Everett
interpretation of quantum states (the so-called preferred basis
problem) (Saunders 1993b, 1995, and Wallace 2003). OSR is also further
elaborated in Ladyman and Ross (2007) and defended against various
criticisms in French and Ladyman (2011). Quantum gravity and
structuralism is discussed by an outstanding collection of
philosophers and physicists in Rickles, French and Saatsi (2006).

Ontic structural realists argue that what we have learned from
contemporary physics is that the nature of space, time and matter are
not compatible with standard metaphysical views about the ontological
relationship between individuals, intrinsic properties and relations.
On the broadest construal OSR is any form of structural realism based
on an ontological or metaphysical thesis that inflates the ontological
priority of structure and relations. The attempt to make this precise
splinters OSR into different forms (three of these are discussed in
Ainsworth (2010) and he argues against two of them), and all of the
following claims have been advocated by some defenders of OSR at some
time:

(1) Eliminativism: there are no individuals (but there is relational
structure)

This view is associated with French and Ladyman. The term
‘eliminative structural realism’ comes from Psillos (2001).
It is criticised on the grounds that there cannot be relations without
relata. This objection has been made by various philosophers including
Cao (2003b), Dorato (1999), Psillos (2001, 2006), Busch (2003),
Morganti (2004) and Chakravartty (1998, 2003) who says: “one
cannot intelligibly subscribe to the reality of relations unless one is
also committed to the fact that some things are related” (1998,
399). In other words, the question is, how can you have structure
without individuals, or, in particular, how can we talk about a group
without talking about the elements of a group? Even many of those
sympathetic to the OSR of French and Ladyman have objected that they
cannot make sense of the idea of relations without relata (see 2004,
Esfeld and Lam 2008, Lyre 2004, and Stachel 2006).

However, there are at least two ways to make sense of the idea of a
relation without relata:

(I) The idea of a universal. For example, when we refer to the
relation referred to by ‘larger than’, it is because we
have an interest in its formal properties that are independent of the
contingencies of its instantiation. To say that all that there is are
relations and no relata, is perhaps to follow Plato and say that the
world of appearances is not properly thought of as part of the content
of knowledge. (See Esfeld and Lam 2008: 5, and the opening
epigram in Psillos 2006.) This Platonic version of OSR is perhaps what
Howard Stein has in mind:

… if one examines carefully how phenomena are
‘represented’ by the quantum theory… then…
interpretation in terms of ‘entities’ and
‘attributes’ can be seen to be highly dubious… I
think the live problems concern the relation of the Forms … to
phenomena, rather than the relation of (putative) attributes to
(putative) entities … (Stein 1989, 59).

(II) The relata of a given relation always turn out to be relational
structures themselves on further analysis. As Stachel puts it,
“it's relations all the way down” (although he denies
the claim, 2006). See, Ladyman and Ross (2007) and Saunders (2003d,
129). The idea that there may be no fundamental level to reality is
discussed in Schaffer (2003).

In any case, eliminativism does not require that there be relations
without relata, just that the relata not be individuals. French and
Krause (2006) argue that quantum particles and spacetime points are
not individuals but that they are objects in a minimal sense, and they
develop a non-classical logic according to which such non-individual
objects can be the values of first-order variables, but ones for which
the law of identity, ‘for all x, x is
identical to x’, does not hold (but neither does
‘x is not identical to x’). There is no
unanimity about the difference between individuals, objects and
entities among philosophers but one neutral way of putting the issue
is to ask whether there are only individual objects in the logical
sense of object as the value of a first-order variable, or whether
there are individuals in some more substantive sense (for example,
being subject to laws of identity, or being substances). Jonathan Bain
(2013) argues that critics of radical ontic structural realism have
implicitly relied on a set-theoretic notion of structure and that a
category theoretic formulation of ontic structural realism is useful
in explicating the structure of physical theories, in particular,
general relativity.

(2) There are relations (or relational facts) that do not supervene
on the intrinsic and spatio-temporal properties of their relata.

The interpretation of entangled states in quantum mechanics in terms
of strongly non-supervenient relations goes back to Cleland (1984).
However, the idea that there could be relations which do not supervene
on the non-relational properties of their relata runs counter to a
deeply entrenched way of thinking among some philosophers. The
standard conception of structure is either set theoretic or
logical. Either way it is often assumed that a structure is
fundamentally composed of individuals and their intrinsic properties,
on which all relational structure supervenes. The view that this
conceptual structure reflects the structure of the world is called
“particularism” by Paul Teller (1989) and “exclusive
monadism” by Dipert (1997). It has been and is endorsed by many
philosophers, including, for example, Aristotle and Leibniz.

Spatio-temporal relations are often exempted from this prescription
since the idea that the position of an object is intrinsic to it is
associated with a very strong form of substantivalism. Hence, the
standard view is that the relations between individuals other than
their spatio-temporal relations supervene on the intrinsic properties
of the relata and their spatio-temporal relations. This is David
Lewis's Humean supervenience:

[A]ll there is to the world is a vast mosaic of local matters of
particular fact, just one little thing and then another …
We have geometry: a system of external relations of spatio temporal
distance between points (of spacetime, point matter, aether or fields
or both). And at these points we have local qualities: perfectly
natural intrinsic properties which need nothing bigger than a point at
which to be instantiated … All else supervenes on that (1986,
x).

Tim Maudlin argues against Lewis's Humean Supervenience on the
basis of quantum entanglement and argues that this means the end of
ontological reductionism, and abandoning the combinatorial conception
of reality that comes from thinking of the world as made of building
blocks, each of which exists independently of the others (1998, 59)
and: “The world is not just a set of separately existing
localized objects, externally related only by space and time”
(60). Similarly, advocates of OSR such as Esfeld, French and Ladyman
emphasise that the non-supervenient relations implied by quantum
entanglement undermine the ontological priority conferred on
individuals in most traditional metaphysics. Some relations are at
least ontologically on a par with individuals so that either relations
are ontologically primary or neither is ontologically primary or
secondary. (Esfeld 2004 and Oliver Pooley 2006 hold the latter view but
Esfeld goes further and claims that if there are intrinsic properties
they are ontologically secondary and derivative of relational
properties (see below).)

(3) Individual objects have no intrinsic natures.

On this view, individual objects of a particular kind are
qualitatively identical. They are not individuated by an haecceity or
primitive thisness. Classical particles can be and often are so
regarded. Classical particles could be so regarded because if a
principle of impenetrability is adhered to, no two such particles ever
have all the same spatio-temporal properties. The bundle theory of
individuation was developed by empiricists to account for the
individuation of physical objects while only quantifying over
properties that are within the reach of natural science. This is a
standard metaphysical position that implies nothing so radical as any
version of OSR. Its interest lies in the fact that on this view it
would seem that the Principle of the Identity of Indiscernibles (PII),
restricted so that identity involving properties are not in its scope,
must be true. If so there are some properties (perhaps including
spatio-temporal properties) that distinguish each thing from every
other thing, and the identity and individuality of physical objects can
be reduced to other facts about them.

The problem is with Quantum Mechanics for it seems there are
entangled quantum states of many particles that attribute exactly the
same intrinsic and relational properties to each of them. For example,
the famous singlet state of two fermions, such as electrons, attributes
to the pair the relation that their spins in any given direction are
opposite to each other, but does not attribute a definite spin in any
direction to either particle alone. Given that they may also be
attributed exactly the same spatial wavefunction, as when they are both
in the first orbit of an atom, for example, then such particles would
seem to violate PII. This leads to a dilemma that was articulated by
Steven French and Michael Redhead (1988); either quantum particles are
not individuals, or they are individuals but the principle of
individuation that applies to them must make reference to some kind of
empirically transcendent haecceity, bare particularity or the like.

Katherine Brading and Alexander Skyles (2012) consider the
plausibility of arguing for structural realism on the basis of this
underdetermination. Saunders argues that there is no
underdetermination (see (5) below). The appeal to this metaphysical
underdetermination is criticised by Chakravartty 2003, who argues that
it cannot be significant since it also obtains in the case of everyday
objects. Morganti (2004) argues in favour of transcendental
individuation, and also points out that if quantum mechanics is not
complete and there are hidden variables as in Bohm theory, the quantum
particles may be individuated by their intrinsic and spatio-temporal
properties after all.

(4) There are individual entities but they don't have any
irreducible intrinsic properties.

Michael Esfeld (2004) rejects (1) and claims that:

(a) relations require relata

but denies that:

(b) these things must have intrinsic properties
over and above the relations in which they stand.

As mentioned above Esfeld holds that there are things and relations
but neither is ontologically primary or secondary. On this view, all
the properties of individual objects are relations to other objects.
This view is called ‘moderate structural realism’ by
Esfeld (and Esfeld and Lam 2008, 2010 and see also their 2012). It
avoids the problems with (1) above, and incorporates (2) and (3). Any
version of (4) that is combined with (3) arguably makes individual
entities ontologically dependent on relational structure (see (6)
below).

Benacerraf (1965) argues that there cannot be objects possessing
only structural properties. The idea of such objects is denounced as
‘mysticism’ by Dummett (1991), and criticised in the
context of structural realism by Busch (2003). These objections go back
to Russell:

…it is impossible that the ordinals should be, as Dedekind
suggests, nothing but the terms of such relations as constitute a
progression. If they are to be anything at all, they must be
intrinsically something; they must differ from other entities as points
from instants, or colours from sounds. What Dedekind intended to
indicate was probably a definition by means of the principle of
abstraction…But a definition so made always indicates some class
of entities having… a genuine nature of their own (1903, p.
249).

On the other hand, D.W. Mertz (1996) defends ‘network instance
realism’ and rejects the ‘tyranny of the monadic’
arguing that individuated relation instances are ontologically
fundamental.

(5) Facts about the identity and diversity of objects are
ontologically dependent on the relational structures of which they are
part.

Saunders (2003a, 2003b and 2006) argues that there is a weakened form
of PII (discussed by Quine 1976) that is satisfied even by electrons
in the singlet state described above. The notion of ‘weak
discernibility’ applies to objects that satisfy some irreflexive
relation (a relation such that xRx does not
obtain for every x). The relation of having opposite spin
that is had by electrons in the singlet state is clearly such an
irreflexive relation and Saunders argues that, since by Leibniz's law,
the holding of an irreflexive relation aRb
entails the existence of distinct relata a and
b, then the electrons are individuals, even though in so far as they
are individuals it is the relations among them that account for
this.

This runs counter to the usual way of thinking according to which
there are individuals in spacetime whose existence is independent of
each other and that facts about the identity and diversity of these
individuals are determined independently of their relations to each
other (Stachel 2006 calls this ‘intrinsic individuality’).
It is widely held that relations between individuals cannot individuate
those same individuals: “relations presuppose numerical diversity
and so cannot account for it”. The argument is that without
distinct individuals that are metaphysically prior to the relations,
there is nothing to stand in the irreflexive relations that are
supposed to confer individuality on the relata. The issue was famously
discussed by Russell (1911), and see also MacBride (2006). Ladyman and
Ross (2007), Saunders (2006) and Stachel (2006) argue that facts about
the identity and diversity of fermions are not intrinsic obtain only in
virtue of the relations into which they enter. On this view the
individuality of quantum particles is ontologically on a par with, or
secondary to the relational structure of which they are parts. Stachel
(2006) calls this ‘contextual individuality’ and he extends
this to spacetime points (see 4.3 below).

Leitgeb and Ladyman (2008) note that in the case of mathematical
structures there is nothing to rule out the possibility that the
identity and diversity of objects in a structure is a primitive
feature of the structure as a whole that is not accounted for by any
other facts about it. Ladyman (2007) also discusses such primitive
contextual individuality. One important question so far not discussed
is whether on the contextualist view the identity and diversity of the
objects depends on the whole structure or just part of it. The
relationship between OSR and PII is assessed in Ainsworth
(2011). Ladyman, Linnebo, and Richard Pettigrew (2013) present some
relevant results in philosophical logic.

(6) There are no subsistent objects and relational structure is
ontologically subsistent.

This claim is associated with quantum holism and holism more generally
(see Horgan and Potrc 2000 and 2002). As mentioned above this is
arguably implied by the conjunction of (3) and (4), and also by (5).
The basic idea of ontological subsistence is that of being able to
exist without anything else existing. The notions of ontological
dependence and ontological subsistence are often employed in
discussions of structuralism but are in need of clarification (see
Linnebo 2008). Kerry McKenzie (forthcoming) uses Fine's recent analyses of
ontological dependence to argue against eliminativist OSR and in
favour of moderate structural realism based on a case study from
particle physics.

(7) Individual objects are constructs

French (1999) and French and Ladyman (2003a) maintain that
individuals have only a heuristic role. Poincaré similarly argued
that “the gross matter which is furnished us by our sensations
was but a crutch for our infirmity” (1898, 41). Ladyman and Ross
(2007) argue that objects are pragmatic devices used by agents to
orient themselves in regions of spacetime, and to construct approximate
representations of the world. Anyone who defends eliminativism as in
(1) above must similarly offer a non-ad hoc account of the point and
value of reference to and generalization over objects in science. For
example, cognitive science may show that we are not able to think about
certain domains without hypostatising individuals as the bearers of
structure. This is as yet mere speculation and a subject for further
study.

The articles in Landry and Rickles (eds.) (2012) explore some of the
above issues. See McKenzie's (2013) review of the collection. See
also the collection Bokulich and Bokulich (eds.) (2011). Joanna Wolff
(2012) considers the relationship between objects and structures,
arguing that the former are not reducible to the latter and suggesting
that a form of ontic structural realism may be defended in terms of
the claim that objects are ontologically dependent on structures.

Group theory was first developed to describe symmetry. A symmetry is
a transformation of some structure or object which leaves it unchanged
in some respect. A group of symmetry transformations is a mathematical
object which consists of the set of transformations, including the
identity transformation and the inverse of each transformation, and the
operation of composing them, where the result of two composed
transformations is itself in the original set. Mathematical objects can
be characterised in terms of which symmetry transformations leave them
unchanged or invariant.

The founders of structuralism shared an appreciation of the
importance of group theory in the ontology of physics. Cassirer held
that the possibility of talking of ‘objects’ in a context
is the possibility of individuating invariants (1944). Similarly, Max
Born says: “Invariants are the concepts of which science speaks
in the same way as ordinary language speaks of ‘things’,
and which it provides with names as if they were ordinary things”
(1953, 149), and: “The feature which suggests reality is always
some kind of invariance of a structure independent of the aspect, the
projection” (149). He goes so far as to say: “I think the
idea of invariant is the clue to a relational concept of reality, not
only in physics but in every aspect of the world.” (144).
Eddington says: “What sort of thing is it that I know? The answer
is structure. To be quite precise it is structure of the kind
defined and investigated in the mathematical theory of groups”
(1939, 147). Poincaré understands group structure in Kantian
terms as a pure form of the understanding.

The idea then is that we have various representations of some
physical structure which may be transformed or translated into one
another, and then we have an invariant state under such transformations
which represents the objective state of affairs. The group structure is
primary and the group representations constructed from this structure
have a derivative status. Representations are extraneous to physical
states but they allow our empirical knowledge of them. Objects are
picked out by the identification of invariants with respect to the
transformations relevant to the context. Thus, on this view, elementary
particles are hypostatisations of sets of quantities that are invariant
under the symmetry groups of particle physics.

For example, one of the most fundamental distinctions between kinds
of particles is that between fermions and bosons. This was described
group theoretically by Weyl and Wigner in terms of the group of
permutations, and the former's approach to relativity theory was
similarly group-theoretic. In the case of quantum mechanics Weyl
asserts that: “All quantum numbers, with the exception of the
so-called principal quantum number, are indices characterising
representations of groups.” (1931, xxi) The central point of
philosophical relevance here is that the mathematical idea of
invariance is taken by Weyl to characterise the notion of objectivity.
It is this that liberates physics from the parochial confines of a
particular coordinate system. For Weyl appearances are open only to
intuition (in the Kantian sense of subjective perception) and therefore
agreement is obtained by giving objective status only to those
relations that are invariant under particular transformations.

Weyl's views have recently been revived by Sunny Auyang (1995) in an
explicitly neo-Kantian project which attempts to solve the problem of
objectivity in quantum mechanics and quantum field theory. Auyang seeks
to extract the “primitive conceptual structure” in physical
theories and she too finds it in what she calls the
“representation-transformation-invariant structure”. This
is essentially group-theoretic structure. Auyang, like Born and Weyl,
thinks that such invariant structure under transformations is what
separates an objective state of affairs from its various
representations, or manifestations to observers under different
perceptual conditions. According to her events are individuated
structurally.

Ryckman (2005) describes the history of relativity theory and Weyl's
role in it. Ryckman argues that the work of Eddington and Weyl was
profoundly influenced by the phenomenology of Husserl. The latter also
seems to have understood objectivity in terms of invariance. (Ryckman
calls Kantian structural realism “transcendental
structuralism”. OSR is what he calls ‘transcendent
structuralism’.) Group theory in the development of
structuralism deserves further historical analysis. It played a
crucial role in epistemological reflections on geometry in relation to
Klein's Erlanger programme (Birkhoff and Bennett 1988). French (1998,
1999, 2000) and Castellani (1998) have explored the ontological
representation of the fundamental objects of physics in terms of sets
of group-theoretic invariants by Cassirer, Eddington,
Schrödinger, Weyl, Wigner, Piron, Jauch and others. On the other
hand, Roberts (2011) criticizes the idea that structure can be
understood as group structure in the context of quantum physics.

Cassirer rejected the Aristotelian idea of individual substances on
the basis of physics, and argued that the metaphysical view of the
‘material point’ as an individual object cannot be
sustained in the context of field theory. He offers a structuralist
conception of the field:

The field is not a ‘thing’, it is a system of effects
(Wirkungen), and from this system no individual element can be
isolated and retained as permanent, as being ‘identical with
itself’ through the course of time. The individual electron no
longer has any substantiality in the sense that it per se est et
per se concipitur; it ‘exists’ only in its relation to
the field, as a ‘singular location’ in it (1936, 178).

In gauge quantum field theories, which are our best contemporary
physical theories of all the forces other than gravity, each theory is
associated with a different symmetry group, and the unification of
theories was achieved by looking for theoretical structures with the
relevant combined symmetry. (For example, the unitary group U(1) for
quantum electrodynamics, U(2) for the unified electroweak theory and
SU(3)/ Z(3) for the strong interaction.) Lyre argues for OSR in the
interpretation of quantum field theory. He argues that “the
traditional picture of spatiotemporally fixed object-like entities is
undermined by the ontology of gauge theories in various ways and that
main problems with traditional scientific realism…can be
softened by a commitment to the structural content of gauge theories,
in particular to gauge symmetry groups” (2004, 666). He goes on
to note that his favoured interpretation of gauge theories (in terms
of non-separable holonomies) is one according to which the fundamental
objects are ontologically secondary to structure because the objects
of a theory are members of equivalence classes under symmetry
transformations and no further individuation of objects is
possible. Similarly, Kantorovich (2003) argues that the symmetries of
the strong force are ontologically prior to the particles that feel
that force, namely the hadrons, and likewise for the symmetries of the
so-called ‘grand unification’ of particle physics in the
standard model. Cao in his book on quantum field theory sometimes
sounds like an ontic structural realist, because he denies that the
structures postulated by field theories must be “ontologically
supported by unobservable entities” (Cao 1997, 5). However, in
his (2003a) he explicitly criticises OSR and argues for a version of
ESR in the context of a discussion of quantum field theory.

Critics of OSR may argue that the claim of metaphysical
underdetermination in the case of non-relativistic many particle
quantum mechanics is resolved by the shift to quantum field theory.
This is especially plausible when it comes to quantum field theory in
a curved spacetime since in that context, “a useful particle
interpretation of states does not, in general, exist” (Wald
1984, 47, quoted in Stachel 2006, 58). See also Malament (1996) and
Clifton and Halvorson (2002), who show that there is a fundamental
conflict between relativistic quantum field theory and the existence
of localisable particles. There are so called unitarily inequivalent
representations of quantum field theories and Howard (2001) argues
that this poses a problem for structural realism, and French (2012)
replies.

Field quantities are usually attributed to space-time points or
regions. The problem of individuality now concerns whether fields
themselves are individuals, or whether they are the properties of
spacetime points. In the latter case the problem becomes whether the
spacetime points are individuals. This last question is bound up with
the debate about substantivalism in the foundations of General
Relativity.

There has been much dispute about whether General Relativity
supports relationism or substantivalism about spacetime. The main
problem for the latter is the general covariance of the field equations
of General Relativity: any spacetime model and its image under a
diffeomorphism (a infinitely differentiable, one-one and onto mapping
of the model to itself) are in all observable respects equivalent to
one another; all physical properties are expressed in terms of
generally covariant relationships between geometrical objects. In other
words, since the points of spacetime are entirely indiscernible one
from another, it makes no difference if we swap their properties around
so long as the overall structure remains the same. This is made more
apparent by the so-called ‘hole argument’ which shows that
if diffeomorphic models are regarded as physically distinct then there
is a breakdown of determinism. Substantivalists cannot just bite the
bullet and accept this since, as John Earman and John Norton (1987)
argue, the question of determinism ought to be settled on
empirical/physical grounds and not a priori ones.

There have been a variety of responses to this problem. Lewis (1986)
and Carol Brighouse (1994) suggest accepting haecceitism about
spacetime points, but argue that it should not worry us that
haecceitistic determinism, that is determinism with respect to which
points end up with which metrical properties, fails. Melia (1999) also
criticises the notion of determinism employed by Earman and Norton.
Nonetheless most philosophers of physics seem to have concluded that if
spacetime points do have primitive identity then the substantivalist
who is committed to them must regard the failure of haecceitistic
determinism as a genuine failure of determinism. Hence, others have
sought to modify the substantivalism.

Robert DiSalle (1994) suggests that the correct response to the hole
argument is that the structure of spacetime be accepted as existent
despite its failure to supervene on the reality of spacetime points. A
similar view has been proposed by Carl Hoefer, who argues that the
problems for spacetime substantivalism turn on the “ascription of
primitive identity to space-time points” (1996, 11). Hence, it
seems that the insistence on interpreting spacetime in terms of an
ontology of underlying entities and their properties is what causes the
problems for realism about spacetime. This is a restatement of the
position developed by Stein (1968) in his famous exchange with
Grünbaum, according to which spacetime is neither a substance, not
a set of relations between substances, but a structure in its own
right. Similarly, Oliver Pooley (2007) argues that eliminativism about
individual spacetime points can be avoided without any tension with
General Relativity, if it is accepted that the facts about their
identity and diversity is grounded in relations they bear to each
other. His sophisticated substantivalism allows that spacetime points
be individuated relationally and not independently of the metric field.
This means embracing contextual individuality grounded in relational
structure. See also Cassirer who says: “To such a [spacetime]
point also no being in itself can be ascribed; it is constituted by a
definite aggregate of relations and consists in this aggregate.”
(1936, 195)

The analogy between the debate about substantivalism, and the debate
about whether quantum particles are individuals was first explicitly
made by Ladyman (1998), but others such as Stachel (2002) and Saunders
(2003a and 2003b) have elaborated it. However, Pooley (2006) argues
that there is no such analogy, or at least not a very deep one, in part
because he thinks that there is no metaphysical underdetermination in
GR. According to him the standard formulations of the theory are
ontologically committed to the metric field, and the latter is most
naturally interpreted as representing “spacetime structure”
(8).

Others who have discussed structural realism and spacetime include,
Dorato (2000) who discusses spacetime and structural realism but
rejects OSR, Esfeld and Lam (2008 and 2012) who argue for moderate ontic
structural realism about spacetime, and Bain (2003), who says that:
“Conformal structure, for instance, can be realised on many
different types of ‘individuals’: manifold points, twisters
or multivectors …What is real, the spacetime structuralist will
claim, is the structure itself and not the manner in which alternative
formalisms instantiate it” (25).

As explained above, there are many different forms of structural
realism and correspondingly, many different objections have been
leveled against it. Obviously, ESR and OSR attract very different
kinds of objections. Different forms of structural realism and
different forms of objections to it are also reviewed in Frigg and
Votsis (2011).
(1) Structural realism collapses into standard realism.

Psillos (1995) argues that any form of structural realism must
presuppose a distinction between the form and content of a theory,
and/or a distinction between our ability to know the structure and our
ability to know the nature of the world. Both these distinctions are
illusory according to Psillos because the scientific revolution
banished mysterious forms and substances that might not be fully
describable in structural terms. For Psillos, properties in mature
science are defined by the laws in which they feature, and “the
nature and the structure of a physical entity form a continuum”
(1995). Hence, for Psillos, structural realism is either false or
collapses into traditional realism. (This is the response of
Richard Braithwaite (1940, 463) to Eddington's structuralism.)
Similarly, David Papineau argues that “restriction of belief to
structural claims is in fact no restriction at all” (Papineau
1996, 12), hence structural realism gains no advantage over traditional
realism with the problem of theory change because it fails to make any
distinction between parts of theories that should and should not enjoy
our ontological commitment. Kyle Stanford (2003, 570) also argues that
we cannot distinguish the structural claims of theories from their
claims about content or natures.

(2) Isn't structure also lost in theory change?

Many people's first response to structural realism is to point out
that mathematical structure is often lost in theory change too (see,
for example, Chakravartty 2004, 164, Stanford 2003,
570–572). The realist is claiming that we ought to believe what
our best scientific theories say about the furniture of the world in
the face of the fact that we have inductive grounds for believing this
will be radically revised, whereas the structural realist is only
claiming that theories represent the relations among, or structure of,
the phenomena and in most scientific revolutions the empirical content
of the old theory is recovered as a limiting case of the new
theory. As Post claimed, there simply are no
‘Kuhn-losses’, in the sense of successor theories losing
all or part of the well confirmed empirical structures of their
predecessors (1971, 229). In sum, we know that well-confirmed
relations among phenomena must be retained by future theories. This
goes beyond mere belief in the empirical adequacy of our theories if
we suppose that the relations in question are genuine modal relations
rather than extensional generalizations about concrete actual
phenomena. However, Newman (2010) argues that structuralism cannot
deal with the pessimistic meta-induction.

(3) Structural realism is too metaphysically revisionary.

The considerations from physics do not logically compel us to
abandon the idea of a world of distinct ontologically subsistent
individuals with intrinsic properties. The identity and individuality
of quantum particles could be grounded in each having a primitive
thisness, and the same could be true of spacetime points. Physics does
seem to tell us that certain aspects of such a world would be
unknowable. The epistemic structural realist thinks that all we can
know is structure, but it is the structure of an unknowable realm of
individuals. An epistemic structural realist may insist in a Kantian
spirit that there being such objects is a necessary condition for our
empirical knowledge of the world. It may be argued that it is
impossible to conceive of relational structures without making models
of them in terms of domains of individuals. Certainly, the
structuralist faces a challenge in articulating her views to
contemporary philosophers schooled in modern logic and set theory,
which retains the classical framework of individual objects, and where
a structure is just a particular set, namely a set of objects, and a
set of relations, where the latter are thought of extensionally as just
sets of ordered pairs (or more generally n-tuples in the case of
n-place relations).

Psillos (2001) argues that OSR is not ‘worked out’ as a
metaphysics, and that a strong burden of proof is on those who would
abandon traditional metaphysics (see also Chakravartty (2004) and
Morganti (2011). However, it is far from clear that OSR's rivals are
‘worked out’ in any sense that OSR isn't. There in no
general agreement among philosophers that any of the metaphysical
theories of, say, universals is adequate, and arguably metaphysical
categories inherited from the ancient Greeks are not appropriate for
contemporary science. Naturalists argue that we should reject
metaphysical doctrines if they are not supported by science. Michael
Esfeld (2004, 614–616) argues against any gap between
epistemology and metaphysics. Similarly Ladyman and Ross (2007) argue
for a kind of verificationism in metaphysics.

In sum, structuralists may agree with what Ernan McMullin says:

[I]maginability must not be made the test for ontology. The realist
claim is that the scientist is discovering the structures of the world;
it is not required in addition that these structures be imaginable in
the categories of the macroworld. (1984, 14)

(4) Structuralists can't account for causation.

Busch (2003), Psillos (2006a) and Chakravartty (2003) all argue that
individual objects are central to productive rather than Humean
conceptions of causation and hence to any genuine explanation of
change. Objects it is alleged provide the ‘active
principle’ of change and causation. French (2006) replies to
this charge invoking the idea of Ladyman (1998 and 2004) and French
and Ladyman (2003) of modal structure, by which is meant the
relationships among phenomena that pertain to necessity, possibility,
potentiality, and probability. Ladyman and Ross (2007) defend a
version of OSR according to which science describes the objective
modal structure of the world, where the latter is ontologically
fundamental, in the sense of not supervening on the intrinsic
properties of a set of individuals. They argue that causal structure
is the pragmatically essential proxy for it in the special sciences
(but not necessarily in fundamental physics). (Ladyman (2008)
considers the causal exclusion argument in this context.) Nora
Berenstain and Ladyman (2012) argue that a commitment to natural
necessity is implicit in arguments for scientific realism and that
realists including structural realists should be anti-Humean and
believe in objective modal structure. See also Esfeld (2009) and for a
Humean take on structural realism, Lyre (2010). The structure of
dispositions described by Mumford (2004) and Psillos's (2003) idea of
nomological structure are cognate to the idea of modal
structure. Giere (1986) first suggested that a form of structural
realism was the result of conjoining modal realism with constructive
empiricism. There is a forthcoming special issue of Synthese
dedicated to examining the relationship between structuralism and
causation. See also the 'final section' of articles on single modality
and causality in structural realism in Landry and Rickles (2012).

This objection is due to Chakravartty (2003) who points out that
certain properties tend to be found together, for example, negative
charge and a certain rest mass, and then asks ‘coincidence or
object?’. French (2006) replies arguing that for a structuralist
objects just are literally coincidences and nothing more. Once again
the challenge for the critic of structuralism is to show that more than
the minimal logical notion of an object is required.

(6) Structural realism only applies to physics.

Gower (2000) argues that structural realism seems less natural a
position when applied to theories from outside of physics. Mark Newman
(2005) argues that structural realism only applies to the mathematical
sciences in therefore cannot account for retention of theoretical
commitments across theory change in, for example, biology. On the
other hand, Harold Kincaid (2008) and Ross (2008) defend structural
realist approaches to the social sciences, as do Ladyman and Ross
(2007). French (2011) considers the implications of ontic structural
realism for the ontology of biology.

(7) Structural Realism collapses the distinction between the
mathematical and the physical.

Many structuralists are motivated by the thought that if mathematics
describes its domain only up to isomorphism, if in other words, it only
describes the structure of the domain, once the scientific description
of the world becomes largely mathematical, then scientific knowledge
too becomes structural knowledge. However, it may then be argued that
if only the structure of mathematical theories is relevant to ontology
in mathematics, and only structural aspects of the mathematical
formalism of physical theories are relevant to ontology in physics,
then there is nothing to distinguish physical and mathematical
structure. Van Fraassen argues that the heart of the problem with OSR
is this:

It must imply: what has looked like the structure of
something with unknown qualitative features is actually all there
is to nature. But with this, the contrast between structure and
what is not structure has disappeared. Thus, from the point of view of
one who adopts this position, any difference between it and
‘ordinary’ scientific realism also disappears. It seems
then that, once adopted, it is not be called structuralism at all!
For if there is no non-structure, there is no structure either. But for
those who do not adopt the view, it remains startling: from an external
or prior point of view, it seems to tell us that nature needs to be
entirely re-conceived. (2006, pp. 292-293)

The essence of van Fraassen's objection here is that the difference
between mathematical (uninstantiated/abstract) structure, and physical
(instantiated/concrete) structure cannot itself be explained in purely
structural terms. There is an analogy here with the theory of
universals and the problem of exemplification. A similar complaint is
made by Cao (2003a and 2003b). Esfeld (2013) uses this objection in
the context of the interpretation of quantum mechanics to pose a
dilemma for ontic structural realism.

Saunders (2003d) points out that there is no reason to think that
ontic structural realists are committed to the idea that the structure
of the world is mathematical. Ladyman and Ross (2007) argue that no
account can be given of what makes the world-structure physical and
not mathematical. On the other hand, Tegmark (2007) explicitly
embraces a Pythagorean form of OSR.

There are two versions of mathematical structuralism: a realist view
according to which mathematical structures exist independently of their
concrete instantiations; and an eliminativist position according to
which statements about mathematical structures are disguised
generalisations about their instantiations that exemplify them (see
Shapiro 1997, 149–50.) For an excellent survey see Reck and Price
(2000). The most well known advocates of realist structuralism in the
philosophy of mathematics are Parsons (1990), Resnik (1997) and Shapiro
(1997). Recent critiques include Hellman (2005) and MacBride (2005).
The relationship between ontic structural realism and ante rem
structuralism has been explored by Psillos (2006a), Busch (2003), French
(2006), Pooley (2006a), Leitgeb and Ladyman (2008), Ladyman
(2007)

Informational structural realism in the context of the foundations of
computer science is defended by Floridi (2008). Structuralism has also
become popular in metaphysics recently in the form of causal
essentialism. This is the doctrine that the causal relations that
properties bear to other properties exhaust their natures. See
Shoemaker (1980) and Hawthorne (2001). Steven Mumford (2004) adopts a
structuralist theory of properties. Alexander Bird's (2007) theory of
dispositions is in some ways structuralist. Anjan Chakravartty's
(2007) deploys dispositional essentialism in the defence of scientific
realism. Michael Esfeld (2011) discusses structuralism about
powers. Finally, Verity Harte (2002) discusses an interesting Platonic
form of structuralism. Alistair Isaac (forthcoming) argues for
structural realism for secondary qualities.

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